General overview of multivariable special functions

TH Koornwinder, JV Stokman - … Functions: The Askey-Bateman …, 2020 - books.google.com
… By classical biorthogonal rational functions we refer to the … (c) By the extension of the
class of classical orthogonal … An important application and source of further applications is …

On a Class of New q-Hypergeometric Expansions as Discrete Analogues of the Erdélyi Type q-Integrals

AV Bhatnagar, Y Vyas - … of Mathematical Modelling, Applied Analysis and …, 2022 - Springer
… problem of finding the discrete extensions of the Erdélyi type q-… The motivation behind this
work is the fact that the q-series … 9} (q)\) biorthogonal rational functions which on specialization …

Elliptic hypergeometric functions

H Rosengren - … Orthogonal Polynomials and Special Functions, 2020 - books.google.com
… of elliptic functions as analogues of rational functions, which … We state an extension of
Theorem 4.12 to elliptic functions of … , they are biorthogonal rational functions. 22 In general, …

[PS][PS] Quasi hypergeometric functions and a few problems related to them

K Aomoto - math.kyushu-u.ac.jp
functions, extensions of the generalized gamma functions are … of validity of the expansion
and applications to harmonic analysis … (x) are rational functions in x with coe cients in Q(q;t). …

Hypergeometric and basic hypergeometric series and integrals associated with root systems

MJ Schlosser - Encyclopedia of Special Functions: The Askey …, 2020 - books.google.com
application of the one-variable q-binomial theorem, it follows that another consequence of
(5.1. 2) is the following An extension … This chapter reviews results for multivariate extensions

Askey–Wilson polynomials and a double 𝑞-series transformation formula with twelve parameters

ZG Liu - Proceedings of the American Mathematical Society, 2019 - ams.org
… –Rahman integral is a very general extension of Euler’s integral representation of the
classical 2F1 function. Based on a q-series transformation formula and the Nassrallah– Rahman …

Extensions of the classical theorems for very well-poised hypergeometric functions

HM Srivastava, Y Vyas, K Fatawat - Revista de la Real Academia de …, 2019 - Springer
… the two most general expansions can be found from … not only permits the derivation of the
extensions of all of the results of … Thus, clearly, the applications of the results of this paper not …

Macdonald-Koornwinder polynomials

JV Stokman - Encyclopedia of Special Functions: The Askey …, 2020 - books.google.com
… From the point of view of applications for instance, symmetric … We determine the biorthogonality
relations of the nonsymmetric … 1) of the affine Hecke algebra and its extension to the …

On some topics based on the concept of coherent pairs of measures of the second kind

M Hancco Suni - 2023 - repositorio.unesp.br
… measures was their applications in connection with the Fourier expansions of functions with
respect … In Chapter 4 we consider the following extension to the study of measures which are …

Integral and series representations of -polynomials and functions: Part III theta, Ramanujan and -Bessel functions

MEH Ismail, R Zhang - Analysis and Applications, 2022 - World Scientific
… The notation for q-series is the same as in [6, 15] or [18]. Part I … Part II dealt with series
expansions and identities related to … 2, we give a common extension of two identities from the Lost …